Some of the Republican Party’s most ardent supporters of the wars in Iraq and Afghanistan have criticized President Barack Obama’s request to launch a limited military strike against Syria.

Former Defense Secretary Donald Rumsfeld, an architect of those earlier wars, thinks Mr. Obama should topple Syrian President Bashar al-Assad or “do nothing.” John Bolton, a former U.S. ambassador to the United Nations, doesn’t think an attack is in the country’s national interest. And Liz Cheney, the Wyoming Senate hopeful and daughter of former Vice President Dick Cheney, said she would vote against a limited strike because Mr. Obama hasn’t developed a plan to intervene.

The debate over using force in Syria has generated plenty of apparent contradictions in both parties. For example, some of the fiercest Democratic critics of the war in Iraq are the ones pushing Congress to grant Mr. Obama the authority to launch a limited military strike against the Assad regime, including Secretary of State John Kerry and Mr. Obama himself. The Syria debate has also unified some of the GOP’s most vocal defense hawks with its increasingly influential libertarian wing.

“You can criticize this from several points of view,” said Sen. Rand Paul (R., Ky.), a leading critic of U.S. military intervention abroad whose father, former Rep. Ron Paul, was the most persistent Republican critic of the Iraq war.

The younger Mr. Paul told reporters Tuesday night that, while he doesn’t believe the conflict in Syria poses a national security threat to the U.S., many of the Republicans who do worry that Mr. Obama’s request doesn’t go far enough. If the resolution “too narrowly defines what the president can do,” Mr. Paul predicted a coalition “of those who are libertarian-leaning” would join with “those who are more neo-conservative leaning” to oppose the president’s request.

That certainly seems to be the case with the former Bush administration officials who oppose the proposed attacks.

“You either ought to change the regime or you ought to do nothing,” Mr. Rumsfeld told the crowd at the Gerald R. Ford Presidential Library in Grand Rapids, Mich., on Tuesday, according to an account on mlive.com. “Why would you go in and fire a shot across the bow? All it does it make a splash. What have you achieved? What you’ve probably achieved is the embarrassment of the United States for being feckless and ineffective.”

Mr. Bolton went a step further. In an appearance on Fox News Tuesday, the former U.N. ambassador said he doesn’t think the use of force “is in America’s interest” and argued that the U.S. should not “in effect take sides in the Syrian conflict.”

Liz Cheney, the daughter of the former vice president who is running to unseat an incumbent Republican in Wyoming, told an audience in the state that she opposes the limited military strike because she doesn’t think the president has offered a defined plan for intervening in the conflict, according to a report in the Jackson Hole News & Guide.

Ms. Cheney, who occupied a State Department post under Mr. Bush to promote democracy in the Middle East, has criticized Mr. Obama for years for failing to pursue more aggressive foreign-policy objectives. She briefly ran a group at State specifically focused on Syria and Iran. After leaving government, she formed a nonprofit with Bill Kristol, a prominent neo-conservative, to inform “concerned Americans about critical national security issues.”

Republicans have a history of opposing previous Democratic efforts to intervene in humanitarian crises. Back in April 1999, the GOP-controlled House defeated a measure authorizing former President Bill Clinton to conduct military strikes against former Yugoslavian republics, with 187 Republicans opposing the measure and just 31 supporting it, including then-Speaker Dennis Hastert (R., Ill.).

“Some member of the GOP are reverting to their more traditional belief that the U.S. military exists to defend the nation for threats, not to do armed social work,” said Christopher Preble, a defense analyst at the libertarian Cato Institute who has questioned cost of a limited military strike. “The Republican rank-and-file is much more skeptical than Republican leaders in Washington of military intervention that is not narrowly focused on advancing vital U.S. national security interests.”

Despite the wave of criticism by members of the previous administration, some Republicans who served in Iraq and Afghanistan are vehemently supporting Mr. Obama’s call to use force in Syria. First-year Arkansas Rep. Tom Cotton, a decorated Army veteran who did stints in Iraq and Afghanistan, and Illinois Rep. Adam Kinzinger, an Air Force pilot who flew missions in both conflicts, expressed their support for the resolution during a House hearing on Wednesday.

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